A shocking coffee connection

There have been some fantastic thunderstorms in London lately. Perhaps nothing to rival thunderstorms in the tropics but for this region of the world they were quite impressive. One lightning storm in particular came very close. Thank goodness for lightning conductors! Perhaps the connection between lightning storms and coffee is not obvious. But maybe this is because you mop up your coffee spillages too quickly.

Reynolds, rain, waves, pond, raining

There are so many coffee-physics connections with rain and weather. It’s worth looking out for more.

The link is in the mess and the maths. It turns out that the maths describing water evaporating out of a drying coffee droplet is the same, in one crucial detail, as the maths describing the electric fields around a lightning conductor. If we want to see why this may be, we need to get a little bit messy and spill some coffee.

The question is how do coffee rings form? We know that to start with the solids in the coffee are distributed fairly evenly throughout the drink. It is the same when you spill it, initially a spilled drop of coffee looks like, well, coffee. But if you wait as this spilled coffee dries, you will find that a ring starts to form around the edge of the drop. How? How does a uniform coffee distribution when the drop is first spilled become a ring of coffee solids around the edge of the dried drop?

coffee ring, ink jet printing, organic electronics

Why does it form a ring?

A number of different aspects of physics feed into this problem but the one that is relevant to the lightning conductors concerns how the water in the drop evaporates. If you think about how a water molecule escapes (evaporates from) the droplet, it is not going to go shooting off like a rocket blasted out from the drop. Instead it will take a step out the drop then encounter a molecule in the air and get deflected to a slightly different path and again, and again, and so on. It follows the same sort of “random walk” that we know that the bits of dust on a coffee surface follow (and the same sort of random walk that provides a link between coffee and the movements of the financial stock exchange but that is a whole other topic).

Now think about the shape of that spilled coffee drop. If a water molecule were to evaporate from the top of the dome of the drop, it has a certain probability of escaping but it also, because its path is random, has a certain probability of re-entering the droplet. A water molecule at the edge of the droplet however will have a lower probability of re-entering the droplet purely on the basis that there isn’t so much of the droplet around it. Over many molecules and many ‘escape attempts’, this lower probability of re-absorption will translate to a higher flux of water molecules evaporating from the droplet at the edges. The water will evaporate ‘more quickly’ from the edge of the droplet than from the top of it.

artemisdraws, evaporating droplet

As the water molecules leave the droplet, they are more likely to escape if they are at the edge than if they are at the top. Image © @artemisworks

When this is written mathematically, the rate of evaporating water is related to the contact angle between the drop and the surface. The shallower the angle, the higher the rate of evaporation or equivalently, the greater the ‘flux’. It is this mathematical expression that is the same as for the lightning conductor if, rather than refer to an evaporating water flux we refer to an electric field. So the more pointy the conductor, the greater the field concentration around it. A shocking example of the idea that everything is connected.

Of course, there is much more to the coffee ring than this with physics that relates coffee rings to bacterial colonies, burning cigarette papers and soap boats. If you are interested, you can read more about how coffee rings form (including why a higher evaporation rate helps lead to a coffee ring effect) here. If on the other hand you want some well justified thinking time, go spill some coffee and watch as the coffee dries.

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